One of the people I often play with simply refuses to believe me when I tell her that it's good to trash copper and estates. She never uses trashing unless it's to trash curses or TFB. She says, "That's just your style of playing", or "You beat us because you practice online not becuase you trash stuff." I'm afraid I'm going to start winning every time (or at least every time that trashing is available) and playing against them won't be as fun. I need new people to play with. (and I highly prefer playing in person to online.)
Then another possibility pops into my head: maybe I'm subconciously keeping myself from getting better to keep it from being less fun...
Maybe telling isn't good enough. "Trashing is good" is a conclusion, not a reason (and not really on obvious conclusion unless you think hard). You probably have to provide multiple, good explanations with simple examples.
Gently suggest after a game that "Trashing Coppers allowed me to see my good cards more often."
Does your family play mostly money strategies? Then they're right! Trashing Coppers actually
is bad for them. If it's the case that they don't stray from Smithy-Big Money (and its variants), then they won't see the benefit of trashing Coppers. Try to explain the speed and power of other non-money strategies.
You have Intrigue, right? Set up a kingdom with Minion, Pawn, and Steward. Explain as you are building a Minion-Pawn deck why trashing Coppers is good: It let's you see Pawns and Minions more often. Minion is clearly better than Copper. Pawn is better than Copper for this strategy, too, because you can get +$1 (and +1 Action) and replace that card when you draw 4 more with Minion netting more than $1 for that card slot. Fewer Coppers mean more Pawns and Minions in hand. In fact, Pawns and Minions are so much better than Copper, that it may be worth spending time early to trash Copper at the expense of better buys. It certainly is if no one competes for Minions with you. (You do have to be a little more careful about always trashing if there is competition for the Minions, though.) This is also a good example of a non-money strategy because you don't even want Silvers if you are uncontested.
If you really want to crank up the crazy, add a Village, Conspirator, and Ironworks. That should all but guarantee a win against money strategies.